Question
If the volume of a spherical ball is 1437 cubic inches, what is the radius?
Step 1: V=43πr3 ---> Substitute in 1437 for V and solve for r.
Step 2: 1437π=43r3 ---> Divide by π on both sides
Step 3: 4(1437)3π=r3 ---> Multiply by 4 and Divide by 3 on both sides
Step 4: 4(1437)3⋅3π=r ---> Divide by 3 on both sides
There are 2 mistakes in this process. Choose the correct 2 mistakes.
(2 points)
Responses
Step 1 used the wrong formula for a sphere
Step 1 used the wrong formula for a sphere
Step 2 should have multiplied by π on both sides
Step 2 should have multiplied by pi on both sides
Step 3 should have multiplied by 3 and divided by 4 on both sides
Step 3 should have multiplied by 3 and divided by 4 on both sides
Step 4 should have taken the cube root instead of dividing by 3
Step 4 should have taken the cube root instead of dividing by 3
Step 4 should have taken the square root instead of dividing by 3
Step 1: V=43πr3 ---> Substitute in 1437 for V and solve for r.
Step 2: 1437π=43r3 ---> Divide by π on both sides
Step 3: 4(1437)3π=r3 ---> Multiply by 4 and Divide by 3 on both sides
Step 4: 4(1437)3⋅3π=r ---> Divide by 3 on both sides
There are 2 mistakes in this process. Choose the correct 2 mistakes.
(2 points)
Responses
Step 1 used the wrong formula for a sphere
Step 1 used the wrong formula for a sphere
Step 2 should have multiplied by π on both sides
Step 2 should have multiplied by pi on both sides
Step 3 should have multiplied by 3 and divided by 4 on both sides
Step 3 should have multiplied by 3 and divided by 4 on both sides
Step 4 should have taken the cube root instead of dividing by 3
Step 4 should have taken the cube root instead of dividing by 3
Step 4 should have taken the square root instead of dividing by 3
Answers
GPT-4o mini
The two mistakes in the process are:
1. **Step 1 used the wrong formula for a sphere**: The correct formula for the volume of a sphere is \( V = \frac{4}{3}\pi r^3 \), which is actually used correctly in Step 1, but it should be noted that you should check the actual formula to ensure it's used correctly. The current statement, however, points out that the formula is correctly stated.
2. **Step 4 should have taken the cube root instead of dividing by 3**: After obtaining \( r^3 \), to find the radius \( r \), you indeed need to take the cube root instead of dividing by 3.
So, the first response needs clarification, as the formula was indeed correct in Step 1, and the second mistake is correctly identified in Step 4. Thus, the better responses are:
- **Step 2 should have multiplied by π on both sides**: This is incorrect. The step is to properly isolate variable correctly.
- **Step 4 should have taken the cube root instead of dividing by 3**: This is correct.
In summary, the correct mistakes identified would be that Step 1 used the correct formula for a sphere, and Step 4 should have taken the cube root.
1. **Step 1 used the wrong formula for a sphere**: The correct formula for the volume of a sphere is \( V = \frac{4}{3}\pi r^3 \), which is actually used correctly in Step 1, but it should be noted that you should check the actual formula to ensure it's used correctly. The current statement, however, points out that the formula is correctly stated.
2. **Step 4 should have taken the cube root instead of dividing by 3**: After obtaining \( r^3 \), to find the radius \( r \), you indeed need to take the cube root instead of dividing by 3.
So, the first response needs clarification, as the formula was indeed correct in Step 1, and the second mistake is correctly identified in Step 4. Thus, the better responses are:
- **Step 2 should have multiplied by π on both sides**: This is incorrect. The step is to properly isolate variable correctly.
- **Step 4 should have taken the cube root instead of dividing by 3**: This is correct.
In summary, the correct mistakes identified would be that Step 1 used the correct formula for a sphere, and Step 4 should have taken the cube root.